src/ZF/Resid/Confluence.ML
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(*  Title:      Confluence.ML
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    ID:         $Id$
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    Author:     Ole Rasmussen
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    Copyright   1995  University of Cambridge
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    Logic Image: ZF
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*)
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open Confluence;
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(* ------------------------------------------------------------------------- *)
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(*        strip lemmas                                                       *)
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(* ------------------------------------------------------------------------- *)
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Goalw [confluence_def,strip_def] 
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    "[|confluence(Spar_red1)|]==> strip";
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by (resolve_tac [impI RS allI RS allI] 1);
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by (etac Spar_red.induct 1);
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by (Fast_tac  1);
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by (fast_tac (claset() addIs [Spar_red.trans]) 1);
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qed "strip_lemma_r";
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Goalw [confluence_def,strip_def] 
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    "strip==> confluence(Spar_red)";
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by (resolve_tac [impI RS allI RS allI] 1);
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by (etac Spar_red.induct 1);
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by (Blast_tac 1);
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by (Clarify_tac 1);
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by (dres_inst_tac [("x1","z")] (spec RS mp) 1);
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by (blast_tac (claset() addIs [Spar_red.trans]) 2);
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by (assume_tac 1);
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qed "strip_lemma_l";
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(* ------------------------------------------------------------------------- *)
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(*      Confluence                                                           *)
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(* ------------------------------------------------------------------------- *)
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Goalw [confluence_def] "confluence(Spar_red1)";
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by (Clarify_tac 1);
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by (ftac simulation 1);
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by (forw_inst_tac [("n","z")] simulation 1);
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by (Clarify_tac 1);
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by (forw_inst_tac [("v","va")] paving 1);
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by (TRYALL assume_tac);
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by (fast_tac (claset() addIs [completeness] addss (simpset())) 1);
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qed "parallel_moves";
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bind_thm ("confluence_parallel_reduction",
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	  parallel_moves RS strip_lemma_r RS strip_lemma_l);
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Goalw [confluence_def] 
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    "[|confluence(Spar_red)|]==> confluence(Sred)";
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by (blast_tac (claset() addIs [par_red_red, red_par_red]) 1);
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val lemma1 = result();
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bind_thm ("confluence_beta_reduction",
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	  confluence_parallel_reduction RS lemma1);
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